Wall pressure spectrum of a low Mach number turbulent boundary layer in the plane for a given frequency : (a) for , (b) for and (c) for .
Sketch of the rotative measurement array, and picture showing the arrangement of the holes on the wall at one end.
Auto-power spectral (APS) densities of wall pressure fluctuations measured by the three kinds of probes under a turbulent boundary layer at and . From bottom to top: — big probes, – – – medium probes and small probes.
Test channel mounted on the outlet of the wind tunnel. The square duct has a width of and a test-section length of a 4 m. The rotating array of remote microphones is located at .
Mean velocity profile (•) and turbulence intensity (▴) measured by hot wire anemometer in the boundary layer at . The transverse distance is normalized by the half-width of the channel, refer to Fig. 4.
Verification test case for a pure tone diffuse sound field, with and . Profile of along the line , post-processing of the theoretical cross-power spectra in solid line, analytical expression given by Eq. (8) in dashed line.
Verification test case for the Corcos model, with , , , and . Profile of along the line . The convected wave number is . — post-processing of the theoretical cross-power spectra, – – – analytical expression given by Eq. (10).
Measured spectrum at in the wavenumber space induced by a turbulent boundary layer.
Acoustical spectral density obtained by integration over the acoustic disk .
Coherence function , see Eq. (11), in the longitudinal direction at . ● experimental data, – – – regression and linear regression.
Computed parameters for the model (12). (a) Convection velocity normalized by the free stream velocity as a function of the frequency. (b) Longitudinal and transversal correlation lengths, in solid line and in dashed line respectively.
Measured auto-power spectral (APS) density in solid line. Acoustic part estimated by integration of over the acoustic disk in dashed line, and acoustic part estimated by Corcos-like model (12) in dotted line.
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